The 21-year-old Tunisian joined United's youth system from Monaco in 2019 and made 13 first-team appearances for the club, scoring once, in a 3-1 defeat to Brighton & Hove Albion last season.
Mejbri has earned 27 caps for his national team and spent the entire of the 2022-23 campaign on loan at Birmingham City.
He returned to Old Trafford at the start of last season but was sent on another loan spell to Sevilla, though he only made six appearances for the La Liga outfit, who opted against exercising their option to permanently sign the midfielder.
However, it seems that the Tunisian international is on the verge of returning to the Championship ahead of the transfer deadline.
Mjebri closing in on move to Turf Moor
Earlier today, transfer expert Fabrizio Romano posted on X: "Hannibal Mejbri completes medical today at Burnley and joins on permanent deal instead of loan with obligation to buy.
"Man United requested change as funds will be received earlier and deal will also include a sell-on clause."
Burnley are believed to view the 21-year-old as a potential long-term replacement for Norwegian international Sander Berge, who recently joined Fulham.
Mejbri is the latest player to depart Old Trafford this summer, following the likes of Facundo Pellistri, Raphael Varane, Anthony Martial, Donny van de Beek, Aaron Wan-Bissaka and Mason Greenwood.
Having entered the final 12 months of his current deal with the Red Devils, Mejbri would have been able to negotiate a free transfer to a new club in January had United not secured a deal for him this summer.
Man United still chasing Ugarte signature
While Man United paid around £4m to sign Mjebri in 2019, he is still regarded as a homegrown asset and his sale will be banked as 'pure profit' as his book value after five years at the club is now the same as an academy player.
Indeed, the funds from the midfielder's sale to Burnley will help United comply with Profit and Sustainability Rules next year, but Erik ten Hag's side may not be done with their summer transfer business just yet.
Recent reports suggest that Man United are close to agreeing a deal worth around £50m for Paris Saint-Germain midfielder Manuel Ugarte.
The Uruguay international has been linked with a move to Old Trafford for several weeks and is believed to be on the verge of making the switch to the Premier League after being left out of Les Parisiens' squad for the first two games of the season.
Ugarte arrived in the French capital at the start of last season from Sporting Lisbon.